Tardive dyskinesia is a involuntary hyperkinetic disorder which usually occurs in older patients after long-term treatment with antipsychotic drugs. These dyskinesias are mostly irreversible and are frequently expressed in the tongue, cheeks, mandible, perioral area and other regions of the face. In this theoretical study we asked the question, why does tardive dyskinesia often have orofacial predominance? What might be the underlying neural network structure which contributes to this propensity? Graph analysis of high-level cortico-striato-thalamo-cortical network structure suggests a connectivity bottleneck. The number of walks of different lengths from the substantia nigra pars reticulata (SNr) to other vertices, as well as the returning cycles are the lowest in the network, which may indicate a higher damage susceptibility of this node. Analysis was also performed on published data from a recent high resolution histological study on cortico-striato-thalamo-cortical networks in rodents. Finer network partitioning and adjacency matrices demonstrated that the SNr has a heterogeneous connectivity structure and the number of local walks from nodes neighboring orofacial neural representation is higher, indicating possible early compensatory escape routes. However, with more extensive SNr damage the larger circuit compensation might be limited. This area of inquiry is important for future research, because identifying key vulnerable structures may provide more targeted therapeutical interventions.